The present disclosure relates to a method for for estimating downhole speed and force variables at an arbitrary location of a moving drill string based on surface measurements of the same variables.
A typical drill string used for drilling oil and gas wells is an extremely slender structure with a corresponding complex dynamic behavior. As an example, a 5000 m long string consisting mainly of 5 inch drill pipes has a length/diameter ratio of roughly 40 000. Most wells are directional wells, meaning that their trajectory and target(s) depart substantially from a straight vertical well. A consequence is that the string also has relatively high contact forces along the string. When the string is rotated or moved axially, these contact forces give rise to substantial torque and drag force levels. In addition, the string also interacts with the formation through the bit and with the fluid being circulated down the string and back up in the annulus. All these friction components are non-linear, meaning that they do not vary proportionally to the speed. This non-linear friction makes drill string dynamics quite complex, even when we neglect the lateral string vibrations and limit the analysis to torsional and longitudinal modes only. One phenomenon, which is caused by the combination of non-linear friction and high string elasticity, is torsional stick-slip oscillations. They are characterized by large variations of surface torque and downhole rotation speed and are recognized as the root cause of many problems, such as poor drilling rate and premature failures of drill bits and various downhole tools. The problems seem to be closely related to the high rotation speed peaks occurring in the slip phase, suggesting there is a strong coupling between high rotation speeds and severe lateral vibrations. Above certain critical rotating speeds the lateral vibrations cause high impact loads from whirl or chaotic motion of the drill string. It is therefore of great value to be able to detect these speed variations from surface measurements. Although measurements-while-drilling (MWD) services sometimes can provide information on downhole vibration levels, the data transmission rate through mud pulse telemetry is so low, typically 0.02 Hz, that it is impossible to get a comprehensive picture of the speed variations.
Monitoring and accurately estimating of the downhole speed variations is important not only for quantification and early detection of stick-slip. It is also is a valuable tool for optimizing and evaluating the effect of remedial tools, such as software aiming at damping torsional oscillations by smart of the control of the top drive. Top drive is the common name for the surface actuator used for rotating the drill string.
Prior art in the field includes two slightly different methods disclosed in the documents US2011/0245980 and EP2364397. The former discloses a method for estimating instantaneous bit rotation speed based on the top drive torque. This torque is corrected for inertia and gear losses to provide an indirect measurement of the torque at the output shaft of the top drive. The estimated torque is further processed by a band pass filter having its center frequency close to the lowest natural torsional mode of the string thus selectively extracting the torque variations originating from stick-slip oscillation. Finally, the filtered torque is multiplied by the torsional string compliance and the angular frequency to give the angular dynamic speed at the low end of the string. The method gives a fairly good estimate of the rotational bit speed for steady state stick-slip oscillations, but it fails to predict speed in transient periods of large surface speed changes and when the torque is more erratic with a low periodicity.
The latter document describes a slightly improved method using a more advanced band pass filtering technique. It also estimates an instantaneous bit rotation speed based upon surface torque measurements and it focuses on one single frequency component only. Although it provides an instantaneous bit speed, it is de facto an estimate of the speed one half period back in time which is phase projected to present time. Therefore it works fairly well for steady state stick-slip oscillations but it fails in cases where the downhole speed and top torque is more erratic.
In addition to giving poor results in transient periods, for example during start-ups and changes of the surface rotation speed, the above methods also have the weakness that the accuracy of the downhole speed estimate depends on the type of speed control. Soft speed control with large surface speed variations gives less reliable downhole speed estimates. This is because the string and top drive interact with each other and the effective cross compliance, defined as the ratio of string twist to the top torque, depends on the effective top drive mobility.